The way our ratios are defined, makes them insensitive to spectral fluxing,
continuum normalization, or reddening. The relation between \(f\) -ratio and
reddening corrected \((J-K_s)_\circ \)  index for the initial sample of 29 514
GALAH stars is illustrated in Fig. REF . The latter shows a
number of highly reddened stars contaminating the sample. To filter them
out we took all stars laying above the knee at \(f\)\(>\) 1.02, and considered
the remaining 15 824 objects (the 15k-sample for short) as representing the
true M-giants present among the 600 255 stars observed by GALAH at the time
of writing of this paper. The \((J-K_s)_\circ \)  colour index has been
calculated from 2MASS photometry and the full extinction as given by
[1]}. The choice of taking the full value of the
tabulated extinction is justified by considering the great distance to our
targets (typically several kpc, beyond which Gaia DR2 or \(e\) DR3 parallaxes
become inaccurate) and their large galactic latitude, which makes their
sight-lines exit the Galactic dust slab well before reaching them.
